Forces, potentials and energy
Separate conservative forces, recoverable energy and dissipation. Follow mechanical, electrical, magnetic and thermal examples, then connect thermodynamic potentials with driving forces.
From physical intuition
to computational practice.
Courses, workshops and learning resources across materials science and scientific computing.
MATERIALS & MECHANISMS
The physical foundations.
- Thermodynamics and Kinetics of Materials (NPTEL) ↗
- Phase Equilibria
- Kinetics of Materials
- Metallic Materials
- Introduction to Micromechanics of Solids
- Transport Phenomena
- Rate Phenomena in Process Metallurgy
MODELS & METHODS
Learning by computing.
- MS5033: Mesoscale Microstructure Modeling
- Computational Methods in Materials Science
- Fundamentals of Scientific Computing
- Introduction to ICME Techniques and Tools
- Machine Learning and Data Analytics in Materials Science
Thermodynamics and
Kinetics of Materials.
My NPTEL course introduces thermodynamics and kinetics for students of metallurgy and materials engineering: thermodynamic potentials, phase equilibria, solutions, chemical reactions, surfaces, reaction rates and diffusion in solids.
A virtual laboratory connects these concepts with calculations of phase equilibria and diffusion using Thermo-Calc’s education package, pycalphad and FiPy.
Open the NPTEL course ↗ACCOMPANYING LECTURE NOTES
Thermodynamics and Kinetics of Materials
These notes follow the NPTEL course and bring together the main ideas, derivations, diagrams and worked examples discussed in the lectures. Short handwritten comments point out useful questions, physical interpretations and common mistakes. I will also add small computational laboratories so that students can explore phase equilibria, diffusion and microstructural evolution for themselves.
THERMODYNAMICS & KINETICS · COMPUTATIONAL LABORATORY
Lab 01: Thermodynamics — From G–X curves to equilibrium phase fractions
You have learned that, when phases are in equilibrium, the chemical potential of each component must be the same in every phase. Together with conservation of each component, this condition helps us calculate equilibrium phase compositions and amounts. In this lab, I show how to use molar Gibbs energy–composition (G–X) curves and a common tangent to do this. The examples include a binary eutectic and standard elemental reference (SER) states. The lab provides plots, seven exercises, worked solutions, self-checks and a coding guide. It uses a simple model and does not require a thermodynamic database.
Open Lab 01: Thermodynamics →
Download Lab 01 notebook ↓
Lab 01 · Thermodynamics · Python · 75–90 minutes · Includes solutions
I will introduce more labs to explore thermodynamics, kinetics and microstructural evolution.
Transport phenomena: notes and laboratories
My Transport Phenomena teaching begins with forces and potentials, develops conservation from finite control volumes to local differential equations, and then connects fluxes with gradients, field tensors, property tensors and material symmetry.
Course materials
Conservation and transport equations
Write a conservation balance for a finite control volume, then derive the local equations for mass, species, energy and momentum. The accompanying note defines the quantities and units and works through a water-tank example.
TensorLab interactive book
Explore field and property tensors, gradient, divergence and curl, and the roles of the Curie and Neumann principles through visual demonstrations.
Transport laboratories
Investigate heat, mass and momentum transport, then test continuity through ducts, tanks, changing density, velocity profiles, oblique surfaces and moving control volumes.
Transport laws and conservation equations
\[\text{potential or state}\ \longrightarrow\ \text{driving force}\ \longrightarrow\ \text{flux}\ \longrightarrow\ \nabla\!\cdot(\text{flux})\ \longrightarrow\ \text{local accumulation}.\]
A potential gradient supplies a driving force, a constitutive relation connects that force with a flux, and the divergence of the flux enters the local conservation law. The details differ for momentum, heat, mass, charge and microstructural evolution, but the definitions and units must be specified for each problem.
Books used alongside the notes and laboratories
- J. F. Nye, Physical Properties of Crystals: Their Representation by Tensors and Matrices. Oxford University Press.
- Robert E. Newnham, Properties of Materials: Anisotropy, Symmetry, Structure. Oxford University Press.
- R. Byron Bird, Warren E. Stewart and Edwin N. Lightfoot, Transport Phenomena. Wiley.
- James R. Welty, Charles E. Wicks, Robert E. Wilson and Gregory L. Rorrer, Fundamentals of Momentum, Heat, and Mass Transfer, 5th edition. Wiley.
OPEN LEARNINGBring the equations
Bring the equations
to the screen.
The Mesoscale Microstructure Modeling library connects concepts with teaching codes, solver documentation and a reproducible worked example.
Explore learning resources ↗COURSE MATERIAL
MS5033: Mesoscale Microstructure Modeling brings together Julia examples, notebooks, assignments and simulation videos. Classroom teaching includes elastic stress effects on microstructural evolution. Access follows the course folder’s Google Drive permissions.
Open MS5033 course materials ↗Beyond the classroom.
MicroSim workshops
KKS-CuFFT, KKS-FD-CUDA-MPI and FFT-based microelasticity models.
Micromechanics for microstructural evolution
Certificate-course teaching at Tata Steel.
Discrete dislocation dynamics
A short course at DMRL, Hyderabad.
Phase-field modeling
Workshops at NIT Srinagar and NRCM lectures at IISc Bangalore.
These are courses and workshops I have taught.